Can you show me a case where it diverges if the initial guess is half the digits of X? Don
On Jan 14, 3:09 am, bharat b <bagana.bharatku...@gmail.com> wrote: > @Don : But, newton's formulae doesn't always converge.. if our guess is bad > enough, it may diverge also. > > > > > > > > On Tue, Jan 8, 2013 at 8:30 PM, Don <dondod...@gmail.com> wrote: > > Sure, > > > Let's try two examples: > > x=1,038,381,081 > > > The last digit is 1, so continue > > Now start with y=10,000 because that is half as many digits as x. > > y0 = 10,000 > > y1 = 56919 > > y2 = 37581 > > y3 = 32605 > > y4 = 32226 > > y5 = 32226 > > y6 = 32223 > > y7 = 32223 > > > Y6=Y7 so you are done. Now square y7 giving 1,038,321,729. That is not > > equal to x, so x is not a perfect square. > > > Second case > > x=1,038,579,529 > > Last digit is 9, so continue. > > y1 = 10000 > > y2 = 56928 > > y3 = 37585 > > y4 = 32608 > > y5 = 32229 > > y6 = 32227 > > y7 = 32227 > > > 32227^2 = x, so x is a perfect square. > > > Don > > > On Jan 5, 8:08 am, bala bharath <bagop...@gmail.com> wrote: > > > @Don, > > > Can u explain with an Example...? > > > > With regards, > > > > Balasubramanian Naagarajan, > > > > Chettinad > > > College of Engg & Tech. > > > > On Sat, Jan 5, 2013 at 1:48 PM, Malathi <malu....@gmail.com> wrote: > > > > Check this. It might help. > > > > >http://www.johndcook.com/blog/2008/11/17/fast-way-to-test-whether-a-n. > > .. > > > > > On Sat, Jan 5, 2013 at 1:47 AM, Don <dondod...@gmail.com> wrote: > > > > >> start with a guess y. If you can arrange for y to be about half the > > > > > -- > > > > > With Regards, > > > > Malathi > > > > > -- > > > -- --
